Finite Group Databasebeta

← #14293342

Subgroups — #14293342

Order 1920.

308 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11750939C211yesmaximal, characteristic
2#11746971C211yesmaximal, characteristic
3#11746924C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic
5C5×#4481C211yesmaximal, characteristic, complemented
6C3×#64702C211yesmaximal, characteristic, complemented
7#11745865C211yesmaximal, characteristic, complemented
8#10599296—31nomaximal, Hall
9C2×#6705—21no—
10C4×D60C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C3×C5×C4⋊C8C2211yescharacteristic
14#91104—21no—
15C4×C3⋊#168C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊#168C2211yescharacteristic
18#90990—21no—
19#90985—21no—
20#90970—21no—
21#90970—21no—
22#90969—21no—
23#90968—21no—
24#68455—51nomaximal, Hall
25#65382—31no—
26#65373—31no—
27#65135—31no—
28#65127—31no—
29C5×#333—31no—
30#64702D311yescharacteristic, complemented
31#64700—31no—
32C2×D60D411yescharacteristic
33C2×C4×D15—21no—
34C2×C5×Dic6—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8—21no—
37C3×C42×C5C2311yescharacteristic
38#6714—21no—
39C4⋊Dic15D411yescharacteristic
40C2×C3⋊#168D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42#6705—42no—
43C5×C4⋊Dic3—21no—
44C5×C4⋊Dic3—21no—
45C2×C5×C3⋊C8—21no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5—21no—
48C2×C3×#168—21no—
49#5087—51no—
50#5079—51no—
51#4842—51no—
52#4838—51no—
53C3×#332—51no—
54#4481D511yescharacteristic, complemented
55#4480—51no—
56C5×C4⋊Q8—31no—
57C2×#676—61no—
58C4×D20—31no—
59#4015C2×D311yescharacteristic
60C5×C4⋊C8—31no—
61C5×C4⋊C8C2×D311yescharacteristic
62#3953—61no—
63#3952—61no—
64#3950—61no—
65#3942—61no—
66#3942—61no—
67#3941—61no—
68#3940—61no—
69C4⋊#168C2×D311yescharacteristic
70C4×#168—31no—
71#1703—151noSylow
72C22×D15—21no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5#4111yescharacteristic
76C2×Dic15—21no—
77D60—21no—
78D60—21no—
79C4×D15—41no—
80C4×D15—41no—
81C2×C5×Dic3—41no—
82C5×Dic6—81no—
83C2×C3×Dic5—41no—
84C3×Dic10—41no—
85C3×Dic10—41no—
86C3×C5×C8—41no—
87C3⋊#168—21no—
88C3⋊#168—21no—
89C3×#168—41no—
90C5×C3⋊C8—41no—
91C3×C4⋊Q8—51no—
92C2×ΓL(1,𝔽25)—101no—
93C4×D12—51no—
94#869C2×D511yescharacteristic
95C3×C4⋊C8—51no—
96C3×C4⋊C8C2×D511yescharacteristic
97#835—101no—
98#835—101no—
99#821—101no—
100(C2×D3)⋊C8—101no—
101#817—101no—
102#809—101no—
103#807—101no—
104C4⋊(C3⋊C8)C2×D511yescharacteristic
105C4×C3⋊C8—51no—
106C2×C5×Q8—61no—
107C2×D20—31no—
108C2×C4×D5—61no—
109C2×Dic10—21no—
110C2×C5×C8—21no—
111C2×C5×C8—61no—
112C5×C4⋊C4—61no—
113C5×C4⋊C4—61no—
114C42×C5C22×D311yescharacteristic
115#685—61no—
116C4⋊Dic5—21no—
117C4⋊Dic5—21no—
118C4⋊Dic5—31no—
119C2×#168—21no—
120C2×#168—31no—
121C2×#168—31no—
122#676—122no—
123#487—151no—
124#476—151no—
125#474—151no—
126#436—151no—
127#334—151no—
128#333—31no—
129#332—51no—
130C22×C3×C5#12111yescharacteristic
131C2×D15—41no—
132C2×D15—41no—
133C2×D15—41no—
134C3×C4×C5—21no—
135C3×C4×C5#13511yescharacteristic
136C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
137C3×C4×C5#13711yescharacteristic
138C3×C4×C5#13711yescharacteristic
139Dic15—41no—
140C3×Dic5—81no—
141C5×Dic3—81no—
142C2×C3×Q8—101no—
143C2×D12—51no—
144C2×C4×D3—101no—
145C2×Dic6—21no—
146C2×C3×C8—21no—
147C2×C3×C8—101no—
148C3×C4⋊C4—101no—
149C3×C4⋊C4—101no—
150C3×C42C22×D511yescharacteristic
151(C2×D3)⋊C4—101no—
152C4⋊Dic3—21no—
153C4⋊Dic3—21no—
154C4⋊Dic3—51no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—51no—
157C2×C3⋊C8—51no—
158ΓL(1,𝔽25)—202no—
159C22×D5—61no—
160C5×Q8—241no—
161C2×C4×C5—121no—
162C2×C4×C5#23511yescharacteristic
163C2×C4×C5D3×D411yescharacteristic
164C2×C4×C5D3×D411yescharacteristic
165C2×Dic5—41no—
166C2×Dic5—61no—
167D20—61no—
168D20—61no—
169C4×D5—121no—
170C4×D5—121no—
171Dic10—41no—
172Dic10—41no—
173C5×C8—41no—
174C5×C8—121no—
175#168—41no—
176#168—61no—
177#168—61no—
178C2×M16—301no—
179C4⋊Q8—31no—
180C4⋊Q8—51no—
181C4×D4—151no—
182#107—301no—
183#106—301no—
184C4⋊C8—31no—
185C4⋊C8—51no—
186C4⋊C8D3×D511yescharacteristic
187#103—301no—
188#103—301no—
189#102—301no—
190#102—301no—
191C22⋊C8—301no—
192C4×C8—151no—
193C2×C3×C5#46311yescharacteristic
194C2×C3×C5#47011yescharacteristic
195C2×C3×C5#47111yescharacteristic
196D15—81no—
197C22×D3—101no—
198C3×Q8—201no—
199C3×Q8—201no—
200C2×C3×C4—201no—
201C2×C3×C4#70911yescharacteristic
202C2×C3×C4D4×D511yescharacteristic
203C2×C3×C4D4×D511yescharacteristic
204C2×Dic3—41no—
205C2×Dic3—101no—
206D12—101no—
207D12—101no—
208C4×D3—201no—
209C4×D3—201no—
210Dic6—81no—
211C3×C8—41no—
212C3×C8—201no—
213C3⋊C8—41no—
214C3⋊C8—101no—
215C3⋊C8—101no—
216C22×C5#88411yescharacteristic
217C2×D5—121no—
218C2×D5—121no—
219C2×D5—121no—
220C4×C5—21no—
221C4×C5—241no—
222C4×C5#91111yescharacteristic
223C4×C5#91511yescharacteristic
224C4×C5#91611yescharacteristic
225C4×C5#91811yescharacteristic
226Dic5—81no—
227Dic5—121no—
228C2×Q8—61no—
229C2×Q8—101no—
230C2×D4—151no—
231C22×C4—301no—
232M16—602no—
233C2×C8—21no—
234C2×C8—61no—
235C2×C8—101no—
236C2×C8—151no—
237C2×C8—151no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—101no—
241C4⋊C4—101no—
242C4⋊C4—151no—
243C22⋊C4—301no—
244C42C2×D3×D511yescharacteristic
245C3×C5#170311yescharacteristic, complemented, Hall
246C22×C3#403011yescharacteristic
247C2×D3—201no—
248C2×D3—201no—
249C2×D3—201no—
250C3×C4—21no—
251C3×C4—401no—
252C3×C4#406011yescharacteristic
253C3×C4#406111yescharacteristic
254C3×C4#406411yescharacteristic
255C3×C4#406511yescharacteristic
256Dic3—81no—
257Dic3—201no—
258C2×C5#475411yescharacteristic
259C2×C5#478711yescharacteristic
260C2×C5#481611yescharacteristic
261D5—241no—
262C23—301no—
263Q8—201no—
264Q8—201no—
265Q8—241no—
266D4—301no—
267D4—301no—
268C2×C4—121no—
269C2×C4—201no—
270C2×C4—301no—
271C2×C4—601no—
272C2×C4—601no—
273C2×C4#677111yescharacteristic
274C2×C4#677711yescharacteristic
275C2×C4#679011yescharacteristic
276C8—41no—
277C8—121no—
278C8—201no—
279C8—301no—
280C8—301no—
281C2×C3#6503711yescharacteristic
282C2×C3#6510511yescharacteristic
283C2×C3#6510811yescharacteristic
284D3—401no—
285C5#6845511yescharacteristic, complemented, Sylow
286C22—601no—
287C22—601no—
288C22—601no—
289C22#9146111yescharacteristic
290C4—21no—
291C4—241no—
292C4—401no—
293C4—601no—
294C4#9127811yescharacteristic
295C4#9128011yescharacteristic
296C4#9149811yescharacteristic
297C4#9152111yescharacteristic
298C3#1059929611yescharacteristic, complemented, Sylow
299C2—1201no—
300C2#1174738311yescharacteristic
301C2#1174795511yescharacteristic
302C2#1174819911yescharacteristic
subgroupG/H
centerC22#91461
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC2×D60D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1703
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #11746924C2semidirect
5. C5×#4481C2semidirect
6. C3×#64702C2semidirect
7. #11745865C2semidirect
30. #64702D3semidirect
54. #4481D5semidirect
245. C3×C5#1703semidirect
285. C5#68455semidirect
298. C3#10599296semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117509392
#117469712
#117469242
#117468852
C5×#44812
C3×#647022
#117458652
#105992963
#684555